I'm a theory geek. I love talking about, reading about, and teaching music theory. It's endlessly fascinating. And I believe it also has very important application to our playing and understanding of music.
Sadly, I find that most adults who come to me after having studied piano as a child (or children who come from other teachers) know next to nothing about theory. They may play a Chopin Nocturne, even quite well, but if I ask them what key it is in, or why it ends a certain way, they have no idea. One could therefore make the argument that it isn't necessary to understand theory to play well. But if you love music, listen to it, play it, maybe even devote a large portion of your life to it, wouldn't you want to understand what makes it work, in fact, what makes it possible?
Music theory is like gravity: it's not just a good idea, it's the law! (Borrowed from a t-shirt I once saw....) Theory isn't some system dreamed up by Pythagoras and imposed on us; it describes the inner laws that govern our (Western) music. Everything our music is built on, from scales and chords, to the forms such as Sonata form, follow laws based on mathematical relationships. How the composer uses those laws create the beauty and power (or lack thereof) of the piece. But he does not invent new laws with every composition; if he did, no one would understand it.
Take for example the Circle of Fifths (if you are not familiar with this concept, you can find a basic, though possibly confusing, explanation on Wikipedia, or refer to a book on music theory). Many people think the Circle of Fifths is just a convenient way to learn or memorize the key signatures of all 12 major and minor keys. But it is much more than that; the fifth is an important interval vibrationally. The closest vibrational relationship between any two tones is an octave, where the relationship of vibrations is 2 to 1 (higher to lower tone). That is why two tones an octave apart sound so similar (not to mention why our whole musical system is based on scales that span an octave). The next closest relationship is between 2 tones a fifth apart, where the ratio of vibrations is 3 to 2. The Greeks called this ratio (3:2) the Golden Mean and considered it the "perfect" relationship. You can find reference to it in the fields of art and architecture; it was said to be the basis of works as diverse as the Ancient Pyramids and the Mona Lisa. In classical music, jazz, and pop, we see the use of the fifth in the progression of chords from one to another and in the modulation from one key to another within a piece. (Note: jazz players call it the Circle of Fourths, which is the same thing as the Circle of Fifths, because a fifth up is the same thing as a fourth down; to me, this always seemed to miss the point, because the relationship of the fifth is more central to music than the fourth. You can get the jazz "Circle of Fourths" by simply going counter-clockwise around the Circle of Fifths.)
My point here is that when one understands the real importance of these aspects of theory, such as the Circle of Fifths, it makes so much of what happens in our music more understandable. Music, like nature, follows certain laws, but within those laws there are infinite possibilities and tremendous variety. But without these laws it would all be chaos and cacophony.
One can learn about theory from text books or dull lecture classes. But if you can't apply it, what use is it? I find the best, and most fun, way to learn a great deal of theory (though certainly not everything) is to learn chords and play songs from fake books. To play from a fake book, you must understand scales and keys, then how chords are constructed (if you really learn how they are constructed -- see my previous post on chords -- not just memorize them from a chord chart), and how the chords progress from one to another. I find it much more fun to actually use your knowledge of harmony by playing it than just to "analyze" a piece of music. I make learning chords and playing from fake books a part of the curriculum of all my students.
Understanding, and more importantly, hearing, how our music obeys certain laws and how each composer uses those laws to create his masterpieces, can be one of those most satisfying aspects of listening to music. Far from making it dry and analytical, it makes you marvel even more at the miracle that is music.